TR-2005-09

On the rank function of the 3-dimensional rigidity matroid

Abstract

It is an open problem to find a good
characterization for independence or, more generally, the rank function
in the d-dimensional rigidity matroid of a graph when d \geq 3.
In this paper we give a brief survey of existing lower and upper
bounds on the rank of the 3-dimensional rigidity matroid of a graph
and introduce a new upper bound,
which may lead to the desired good characterization.